Solve for $x$ and $y$ using elimination. $\begin{align*}-6x+y &= -4 \\ 8x+3y &= 1\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-3$ and the bottom equation by $1$ $\begin{align*}18x-3y &= 12\\ 8x+3y &= 1\end{align*}$ Add the top and bottom equations. $26x = 13$ Divide both sides by $26$ and reduce as necessary. $x = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $x$ in the top equation. $-6( \dfrac{1}{2})+y = -4$ $-3+y = -4$ $y = -1$ $y = -1$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = -1$.